Question

question
the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $1 \leq x \leq 6$?

Explanation:

Step1: Identify f(1) from graph

From the graph, when $x=1$, $f(1)=-4$

Step2: Identify f(6) from graph

From the graph, when $x=6$, $f(6)=-12$

Step3: Apply average rate formula

The average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=1$, $b=6$, $f(1)=-4$, $f(6)=-12$.
$\text{Average rate of change} = \frac{f(6)-f(1)}{6-1} = \frac{-12 - (-4)}{5}$

Step4: Calculate the result

Simplify the numerator first: $-12 - (-4) = -12 + 4 = -8$. Then divide by 5: $\frac{-8}{5} = -1.6$

Answer:

$-1.6$ or $\boldsymbol{-\frac{8}{5}}$